The amount in dollars, A, spent weekly by a household on food is a function of the household's weekly income in dollars, I, and the number of people in the household, n. Thus, . If A_I (1000, 4) = a 0, then which of the following is true? A)At a weekly income of $1000 and a household size of 4, an increase of 1 person in the household produces a decrease of $a in the amount spent weekly on food. B)At a weekly income of $1000 and a household size of 4, an increase of $1 in weekly income produces a decrease of $a in the amount spent weekly on food. C)At a weekly income of $1000 and a household size of 4, an increase of 1 person in the household produces an increase of $a in the amount spent weekly on food. D)At a weekly income of $1000 and a household size of 4, an increase of $1 in weekly income produces an increase of $a in the amount spent weekly on food.

Question

The amount in dollars, A, spent weekly by a household on food is a function of the household's weekly income in dollars, I, and the number of people in the household, n. Thus, . If A_I (1000, 4) = a > 0, then which of the following is true? A)At a weekly income of $1000 and a household size of 4, an increase of 1 person in the household produces a decrease of $a in the amount spent weekly on food. B)At a weekly income of $1000 and a household size of 4, an increase of $1 in weekly income produces a decrease of $a in the amount spent weekly on food. C)At a weekly income of $1000 and a household size of 4, an increase of 1 person in the household produces an increase of $a in the amount spent weekly on food. D)At a weekly income of $1000 and a household size of 4, an increase of $1 in weekly income produces an increase of $a in the amount spent weekly on food.

Quizplus · Accepted Answer

The given function is A(I,n) = In^(3/4). To find a, we need to differentiate the function partially with respect to I, holding n constant.
A'(I,n) = n^(3/4)
At I=1000 and n=4, a = A'(1000,4) = 2
Therefore, an increase of $1 in weekly income (which is the same as an increase of $1000 in I) produces an increase of $2 in the amount spent weekly on food, holding n constant. Hence, the correct choice is D.

The Amount in Dollars, A, Spent Weekly by a Household